Matrix Operations Underlying the Transformer Models
Session
Computer Science and Communication Engineering
Description
This paper explores the mathematical principles underlying the transformer model, an architecture that is driving the advancement of artificial intelligence (AI). While older processing models like Recurrent Neural Networks and Long Short-Term Memory Networks struggled with long range dependencies and parallel computations, transformers overcome these challenges through self attention and parallelism. The core of this architecture lies matrix operations, specifically matrix multiplication and the dot product, which allow transformers to capture relationships across sequences.This paper first walks us through the traditional sequential models, then outlines the encoder, decoder and encoder-decoder variations that define the modern transformer architecture. We then focus on Query, Key and Value matrices within the attention mechanism, and illustrating the computation of attention using embedding vectors and weight matrices through a concrete example.By focusing on the linear algebra underlying transformer models, this paper shows how mathematical operations ensure efficiency and performance in natural language processing (NLP) and beyond. Understanding these fundamental mathematical principles clarifies how transformers work and provides insight into the future of AI.
Keywords:
Artificial Intelligence, Decoder, Dot Product, Encoder, Long Short-Term Memory Networks (LSTMs), Matrix, Matrix Multiplication, Natural Language Processing (NLP), Recurrent Neural Networks (RNNs), Self Attention, Transformer
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-982-41-2
Location
UBT Kampus, Lipjan
Start Date
25-10-2025 9:00 AM
End Date
26-10-2025 6:00 PM
DOI
10.33107/ubt-ic.2025.84
Recommended Citation
Leka, Hizer and Leka, Albiona, "Matrix Operations Underlying the Transformer Models" (2025). UBT International Conference. 16.
https://knowledgecenter.ubt-uni.net/conference/2025UBTIC/CS/16
Matrix Operations Underlying the Transformer Models
UBT Kampus, Lipjan
This paper explores the mathematical principles underlying the transformer model, an architecture that is driving the advancement of artificial intelligence (AI). While older processing models like Recurrent Neural Networks and Long Short-Term Memory Networks struggled with long range dependencies and parallel computations, transformers overcome these challenges through self attention and parallelism. The core of this architecture lies matrix operations, specifically matrix multiplication and the dot product, which allow transformers to capture relationships across sequences.This paper first walks us through the traditional sequential models, then outlines the encoder, decoder and encoder-decoder variations that define the modern transformer architecture. We then focus on Query, Key and Value matrices within the attention mechanism, and illustrating the computation of attention using embedding vectors and weight matrices through a concrete example.By focusing on the linear algebra underlying transformer models, this paper shows how mathematical operations ensure efficiency and performance in natural language processing (NLP) and beyond. Understanding these fundamental mathematical principles clarifies how transformers work and provides insight into the future of AI.
